| WhyDoJournalistsLoveStupidEquations Recorded at the British Science Festival 2009l Keywords: Maths Downloads: 8 |

| maths_479 mathes reflection Keywords: maths Downloads: 17 |

| String Theory for Undergraduates- Lecture 4 - Alan Guth;Barton Zwiebach
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| Thermal Energy- Part0 - Prelude- Review of Unified Engineering Thermodynamics - Zoltan Spakovszky
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| Complex Multiplication - James S. Milne These are preliminary notes for a modern account of the theory of complex multiplication. A shortened (minimal) version will be included in my book on Shimura varieties, and a complete longer version may one day be published separately. Keywords: Maths Downloads: 23 | |

| Theory of Probability- Laws of Large Numbers. - Dmitry Panchenko
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| Advanced Analytic Methods in Science and Engineering- Separation of Variables - Hung Cheng In this chapter, we shall discuss the method of separation of variables and demonstrate this method with several PDEs examples. Keywords: Maths Downloads: 8 | |

| Analysis I- Construction of R - Katrin Wehrheim The idea is, a real number is a sequence of rational ap_proximations. But we have to be careful since, as we saw above, very different sequences of rational numbers can equally well approximate the same real number. To take care of this ambiguity, we will have to de�ne real numbers as sets of rational approximating sequences, all with the same tail behaviour. To make this precise, the following section contains precise de�nitions and some theorems which we will need to set out the formal mat... Keywords: Maths Downloads: 22 | |

| Mathematical Methods for Engineers II- Solving Large Linear Systems - Gilbert Strang Here is another good ordering, di_erent from minimum degree. Graphs or meshes are often separated into disjoint pieces by a cut. The cut goes through a small number of nodes or meshpoints (a separator). It is a good idea to number the nodes in the separator last. Elimination is relatively fast for the disjoint pieces P and Q. It only slows down at the end, for the (smaller) separator S. Keywords: Maths Downloads: 19 | |

| Thermal Energy- Part1C - Applications of The Second Law - Zoltan Spakovszky
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| Lecture Notes in Statistical Mechanics- - Tables - Igor Vilfan This document consists of tables only Keywords: Maths Downloads: 12 | |

| General Relativity (Notes for Px436) - Tom Marsh These notes mostly show the essentials of the lectures, i.e. what I write on the board. The exception to the rule is when I write pieces of text like this (outside of the examples). These represent information that I may have said but not written during lectures. I use them when I think it would help you follow the notes. The notes are very terse, and brief to the point of grammatical inaccuracy.This is because they are notes and are not intended to replace books... Keywords: Maths Downloads: 15 | |

| Relativity- Relativistic Dynamics - Max Tegmark Topics: Formula summary � Momentum & energy � Acceleration & force (optional) � Transformation of force (optional) � Transformation of acceleration (optional) Keywords: Maths Downloads: 23 | |

| General Physics II- Nuclear Physics - Mr. Travis Byington;Lawrence Evans;Mr. Ryan Magee;Hao Zhang Overview - The discovery of radioactivity in 1896 caused a shock among chemists, because it suggested that the atom is not the eternal, immutable object they assumed it to be. This became even clearer within a few years, when radioactive process were studied carefully and it was shown that, in some of them, existing elements in the sample under study disappeared and were replaced by others that had not previously been there... Keywords: Maths Downloads: 13 | |

| Colliding Plane Waves in General Relativity- Chapter 12 - Solution-Generating Techniques - Jerry Griffiths In this chapter we will consider only vacuum solutions. This will enable us to continue to concentrate on the collision of gravitational waves. Various techniques will be discussed here, and the main solutions that have been obtained using them will be described in the next chapter. Many techniques are also known by which solutions of the Einstein�Maxwell equations, and other non-vacuum solutions, can be generated from known vacuum solutions... Keywords: Maths Downloads: 11 | |

| Special Relativity - I - Elizabeth Stanway Objectives: (1) To recap some basic aspects of SR (2) To introduce important notation. Keywords: Maths Downloads: 10 | |

| Lecture Notes in Statistical Mechanics- Lecture 4B - The Renormalization Group Methods - Igor Vilfan Some typical results of MC simulations of a d = 2 Ising ferromagnet are shownin Fig. 4.9. At high T (T = 2TC), there is only short-range order, the spins form small clusters. The correlation length (approximately equal to the linear size of the largest cluster) is small. Close (but above) TC, somewhat larger patches in which most of the spins are lined up in the same direction begin to develop. ... Keywords: Maths Downloads: 25 | |

| Theory of Probability- Martingales. Doob's Decomposition. Uniform Integrability. - Dmitry Panchenko
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| General Physics I- Rotational Motion 2 - Lawrence Evans;Mr. J. Edward Ladenburger Torque Motion of a rigid body, like motion of any system of particles, is changed by the effects of external forces. A rigid body's motion consists of motion of the CM plus rotation about the CM; external forces can change one or both of these parts of the motion. Keywords: Maths Downloads: 10 | |

| Special Relativity - II - Elizabeth Stanway Objectives: Four vectors Keywords: Maths Downloads: 11 | |

| Quantum Condensed Matter Field Theory- Lecture 7 - Quantum Magnetism and The Ferromagnetic Chain - Ben Simons Following on from our investigation of the phonon and interacting electron system, we now turn to another example involving bosonic degrees of freedom � the problem of quantum magnetism. Keywords: Maths Downloads: 15 | |

| Critical Phenomena, Phase Transitions, and Statistical Field Theory- Critical Phenomena, Phase Transitions, and Statistical Field Theory - R.R. Horgan These notes are concerned with the physics of phase transitions: the phenomenon that in particular environments, qualified by particular values of external parameters such as temperature, magnetic field etc., many systems exhibit singularities in the thermodynamic variables which best describe the macroscopic state of the system. For example... Keywords: Maths Downloads: 25 | |

| Post-Newtonian Theory- Post-Newtonian Theory for The Common Reader - Eric Poisson
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| Statistical Physics- Classical Thermodynamics - David Tong So far we�ve focussed on a statistical mechanics, studying systems in terms of their microscopic constituents. In this section, we�re going to take a step back and look at classical thermodynamics. This is a theory that cares nothing for atoms and microscopics. Instead it describes relationships between the observable macroscopic phenomena that we see directly. Keywords: Maths Downloads: 33 | |

| Differential Equations - Stability - John Lewis;Arthur Mattuck;Haynes Miller;Jeremy Orloff A system is called stable if its long-term behavior does not depend signi�cantly on the initial conditions. It is an important result of mechanics that any system of masses connected by springs (damped or undamped) is a stable system. In network theory, there is a similar result: any RLC-network gives a stable system. In these notes, we investigate for the simplest such systems why this is so. Keywords: Maths Downloads: 15 | |

| Theory of Probability- Convergence of Martingales. Fundamental Wald's Identity. - Dmitry Panchenko
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| Colliding Plane Waves in General Relativity- Chapter 6 - The Field Equations - Jerry Griffiths The colliding wave problem has been described in terms of two approaching waves in regions II and III, in a background region I, which is here taken to be �at. According to the work of Penrose (1980), the initial data are well set, so that a unique solution exists in the interaction region IV at least in the neighbourhood of the boundaries of regions II and III. It is therefore necessary �rst to state the relevant �eld equations in the interaction region, and then to attempt to solve them ... Keywords: Maths Downloads: 16 | |

| General Physics I- Wave Motion 3 - Lawrence Evans;Mr. J. Edward Ladenburger Standing waves in a string. We consider again two harmonic waves with the same amplitude, wavelength and frequency, but now moving in opposite directions. Keywords: Maths Downloads: 20 | |

| General Physics I- Thermal Physics 3 - Lawrence Evans;Mr. J. Edward Ladenburger
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| Colliding Plane Waves in General Relativity- - Introduction - Jerry Griffiths The subject to be discussed in this book is the collision and interaction of gravitational and electromagnetic waves. This is a particularly importanttopic in general relativity since the theory predicts that there will be a non-linear interaction between such waves. The e_ect of the non-linearity, however, is unclear. It is appropriate therefore to look in some detail at the simplest possible situation in which the e_ect of the non-linearity will be manifest: namely the interaction between coll... Keywords: Maths Downloads: 17 | |

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| The Works Of Brett Nortje Maths maths. Keywords: maths Downloads: 11 | |

| Optical Physics and Quantum Electronics- Elementary Laser Models - Rate Equation Approach - R. Victor Jones Population Inversion and "Lasering" in a Three-Level System: Obviously, the trick in building masers and lasers has been to find means to "invert" the equilibrium population of states. First conceived by Charles Townes in 1951, Gordon, Zeiger and Townes in 1954... Keywords: Maths Downloads: 24 | |

| Quantum Physics I- Lecture6 - Vladan Vuletic Photoelectric e_ect Observed 1888; explanation, Einstein 1905. A negatively charged metal plate loses charge slowly if illuminated with light, while a positive charge remains. Light of su_ciently short wavelength releases electrons, the electron current is proportional to the intensity of the light. Light below a certain cut o_ frequency _0 does not release any electrons, no matter how high the intensity... Keywords: Maths Downloads: 15 | |

| Electromagnetic Fields, Forces, and Motion- Lecture 1 - Integral Form of Maxwell�s Equations - Markus Zahn
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| Lectures on Quantum Field Theory - Lecture 6 - Quantum Electrodynamics - David Tong In this section we �nally get to quantum electrodynamics (QED), the theory of light interacting with charged matter. Our path to quantization will be as before: we start with the free theory of the electromagnetic �eld and see how the quantum theory gives rise to a photon with two polarization states. We then describe how to couple the photon to fermions and to bosons. Keywords: Maths Downloads: 15 | |

| Mathematics for Computer Science - Random Variables and Distributions - Albert R. Meyer An indicator random variable is a random variable that maps every outcome to either 0 or 1. Indicator random variables are also called Bernoulli variables. Keywords: Maths Downloads: 17 | |

| Seminar in Geometry- Chapter 16- Manifolds and Geodesics - Emma Carberry
Keywords: Maths Downloads: 12 | |

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| Quantum Condensed Matter Field Theory- Lecture 21 - Cooper instability - Ben Simons In the �nal section of the course, we will explore a pairing instability of the electron gas which leads to condensate formation and the phenomenon of superconductivity. Keywords: Maths Downloads: 22 | |

| Statistical Physics- Classical Gases - David Tong Our goal in this section is to use the techniques of statistical mechanics to describe the dynamics of the simplest system: a gas. This means a bunch of particles, �ying around in a box. Although much of the last section was formulated in the language of quantum mechanics, here we will revert back to classical mechanics. Nonetheless, a recurrent theme will be that the quantum world is never far behind: we�ll see several puzzles, both theoretical and experimental, which can only truly be reso... Keywords: Maths Downloads: 19 | |

| Quantum Condensed Matter Field Theory- Lecture 16 - Applications and Connections - Ben Simons Partition Function of ideal (Non-Interacting) Gas of Quantum Particles Useful for �normalisation� of interacting theories Keywords: Maths Downloads: 12 | |

| New Results in Topological Field Theory and Abelian Gauge Theory- New Results in Topological Field Theory and Abelian Gauge Theory - George Thompson These are the lecture notes of a set of lectures delivered at the 1995 Trieste summer school in June. I review some recent work on duality in four dimensional Maxwell theory on arbitrary four manifolds, as well as a new set of topological invariants known as the Seiberg-Witten invariants. Much of the necessary background material is given, including a crash course in topological �eld theory, cohomology of manifolds, topological gauge theory and the rudiments of four manifold theory... Keywords: Maths Downloads: 16 | |

| Nonlinear Optics- Lecture 8 - Fredrik Jonsson In this lecture, the electric polarisation density of the medium is �nally inserted into Maxwell�sequations, and the wave propagation properties of electromagnetic waves in nonlinear optical media is for the �rst time in this course analysed. As an example of wave propagation in nonlinear optical media, the optical Kerr e_ect is analysed for in�nite plane continuous waves.The outline for this lecture is:� Maxwells equations (general electromagnetic wave propagation)� Time dependent p... Keywords: Maths Downloads: 23 | |

| General Physics II- Magnetostatics 1 - Mr. Travis Byington;Lawrence Evans;Mr. Ryan Magee;Hao Zhang We begin our discussion with magnetic �elds that are static, i.e., independent of time. The �eld is de�ned by its effect on a moving point charge. Then we discuss steady currents as sources of magnetic �elds, exploring some useful and important special con�gurations of currents. Later on we will discuss another important source of magnetic �elds, an electric �eld that is changing with time. Keywords: Maths Downloads: 14 | |

| Physics I- Classical Mechanics - Angular Momentum and Torque for a System of Particles - Peter Dourmashkin
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| Linear Partial Differential Equations Analysis and Numerics- The Heat and Wave Equations in 2D and 3D - Matthew Hancock We now consider the special case where the subregion D is the unit circle (we may assume the circle has radius 1 by choosing the length scale l for the spatial coordinates as the original radius): ... Keywords: Maths Downloads: 32 | |

| Thermodynamics & Statistical Mechanics- an Intermediate Level Course - Richard Fitzpatrick In this course, we shall focus almost exclusively on those physical properties of everyday materials which are associated with the motions of their constituent atoms or molecules. In particular, we shall be concerned with the type of motion which we normally call �heat.� We shall try to establish what controls the �ow of heat from one body to another when they are brought into thermal contact... Keywords: Maths Downloads: 42 | |

| Relativity- Symmmetry & Invariance - Max Tegmark Topics: The notion of symmetry in physics. Key concepts: � � Frame � Inertial frame � Transformation � Invariant � Invariance � Symmetry � Relativity Examples of possible symmetry: � � Translation � Rotation � Parity � Galilean � Lorentz � Di_eomorphism � Gauge We will study the symmetry of: � � Classical mechanics � both initial conditions (v, E, etc.) and laws � Electromagnetism � in particular _ The wave equation _ Observed properties of light � doe... Keywords: Maths Downloads: 30 | |